Thousands of protesters clashed in India's eastern city of Kolkata on Wednesday as demonstrations seeking justice for a murdered doctor spiralled into violent street skirmishes between political rivals.

The discovery of the 31-year-old doctor's body at a state-run hospital in Kolkata on August 9 stoked nationwide anger over the chronic issue of violence against women.

That sparked strikes by medics and rallies backed by thousands of ordinary citizens across India, although many doctors have since returned to work.

But repeated protests in West Bengal state capital Kolkata have transformed into clashes between the state's ruling All India Trinamool Congress (AITMC) and the opposition Bharatiya Janata Party (BJP).

The Hindu-nationalist BJP is the party of Prime Minister Narendra Modi and holds power nationally, but sits in opposition in West Bengal.

"We want justice", BJP supporters chanted, referring to the murdered doctor, then demanding the resignation of AITMC leader Mamata Banerjee, the chief minister.

"Go back! Go back!" AITMC supporters shouted in return.

On Tuesday, police clashed with protesters, firing tear gas canisters and water cannons, and arresting at least 245 people.

That prompted BJP supporters on Wednesday to launch a day-long shutdown of Kolkata, with skirmishes against AITMC supporters in the morning.

Protesters erected barricades to close roads and railway lines, with police reporting clashes between rival workers across the city and in adjoining districts.

One man has been detained for the murder, but Banerjee's government has faced public criticism for the handling of the investigation.

India's Supreme Court has ordered a national task force to examine how to bolster security for healthcare workers, saying the "horrific" killing had "shocked the conscience of the nation". (AFP)